Heat conduction worksheet with answers

Free printable Heat conduction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Mineral wool, k = 0.0410 mm15 °C-7 °CQ̇ = ?

A wall of mineral wool is 10 mm thick and has an area of 8 m². Its faces are held at 15 °C and -7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 10 mmA = 8 m²T1 = 15 °CT2 = -7 °C
Q̇ = W
2.Easy
Wood, k = 0.17100 mm24 °C1 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 20 m². Its faces are held at 24 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 20 m²T1 = 24 °CT2 = 1 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035250 mmGlass, k = 0.96100 mm24 °C-5 °CQ̇ = ?

A wall is made of 250 mm of expanded polystyrene and 100 mm of glass, with an area of 4 m². The outer faces are at 24 °C and -5 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 24 °CT3 = -5 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0475 mm22 °C1 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 75 mm of mineral wool, with an area of 12 m². The outer faces are at 22 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 12 m²T1 = 22 °CT3 = 1 °C
Ti = °C
5.Hard
Concrete, k = 1.450 mmExpanded polystyrene, k = 0.035100 mmroom 22 °Coutside 4 °CTs​ = ?Q̇

A wall of 50 mm concrete and 100 mm expanded polystyrene separates a room at 22 °C from outside air at 4 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 4 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17150 mmConcrete, k = 1.450 mmroom 21 °Coutside -12 °CQ̇

A wall of 150 mm gypsum board and 50 mm concrete separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -12 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 704 W
  2. 2. Q̇ = 782 W
  3. 3. Q̇ = 16.01 W
  4. 4. Ti = 12.92 °C
  5. 5. Ts = 21.26 °C
  6. 6. U = 0.8891 W/(m²·K)

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